1. Field of the Invention
This invention relates to an approximation method for shape data, particularly with normal vectors and a drawing device which are adapted for reducing the complexity of the shape, and with respect to shape data with normal vectors expressing a geometric model used in computer graphics (CG).
2. Description of the Related Art
In drawing by so-called computer graphics (CG), in general, a same model is constantly used regardless of the position, size and depth of the model, the point of a viewer's attention, and the shifting speed of the model.
However, the same model is not always required for drawing. By switching the model in accordance with the position, size and depth of the model within a screen, the point of the viewer's attention, and the shifting speed of the model, and using a more simplified model as well as an original detailed model, sufficient picture quality may be obtained.
For example, if a model is located at a distant position, the size of the model on the screen is so small that minute uneven changes of the original model are not seen. Also, with respect to a model located outside of the viewpoint of the viewer, detailed portions need not be seen. In addition, if the mode shifts within the screen at a high speed or if no attention should be paid to the model, detailed portions of the model need not be seen, either.
That is, in such cases, it is not necessary to perform drawing by using the detailed original model. It suffices to use an approximated model from which detailed portions of the original model have been removed.
With a model as a drawing target, a normal is allocated to each surface and vertex, and drawing is performed based on the assumption that a light is radiated to the model. In this way, the quality of drawing results is generally improved. This technique produces results similar to those in the case where a light is actually radiated to the model, by calculating reflectance and refraction in the case where the light is radiated.
Therefore, in performing shape approximation as described above, it is necessary to pay attention to the normals allocated to the surfaces and vertices of the model. There should not be any inconvenience, such as, increase in the entire operation quantity as a result of preventing deterioration in appearance of the model due to an erroneous direction or value of the normal at the time of approximation, or as a result of duplicate operations for re-allocating the normal to the approximated model.
Meanwhile, with respect to shape approximation, a trial of hierarchical approximation of a polygon model is described, for example, in the literature "Re-tiling polygonal surface" (computer graphics, Vol.26, No.2, July 1992) by Greg Turk. In this literature, however, the normal allocated to each vertex and surface of the model is not considered. In "Mesh Optimization" (Computer Graphics Proceedings, Annual Conference Series, SIGGRAPH 1993) by Hugues Hoppe, et al., energy is introduced in evaluation of an approximated model, and the model is approximated by repeating removal of an edge, division of a patch and swapping of the edge so that the energy is minimized. However, the normal vector at the time of approximation is not considered in this technique, either. Therefore, duplicate processing for providing normal vectors to an approximated model after the approximation of the model is required.
As described above, the past studies have some problems in model approximation.
Specifically, in the conventional approximation technique for geometric models used for CG, deterioration in quality after approximation has not been prevented by processing, such as, removal of the normal allocated to the model or change of value of the normal. Also, no particular measures have been taken to eliminate the necessity of re-allocating the normal after approximation. Approximation in consideration of the normal vectors themselves has not been done.
In view of the foregoing status of the art, it is an object of the present invention to provide a shape data approximation method and a drawing device which enable approximation of a geometric model used for CG in a state that normal vectors are appended, and which enable prevention of distortion of the normal vectors in approximation results.